HISTORY and mystery – that’s the intriguing combo Ricky Jay is offering in his latest one-man show “Ricky Jay: On the Stem.”

From a theater on 43rd Street, Jay speaks nostalgically, lovingly, learnedly of the old Times Square – a world that jumbled together Lunt and Fontanne with cheap magic shows, Yiddish theater (it offered “Hamlet Improved”) and flea-circus spectacles.

Jay, a heavy but light-moving man dressed in a dapper black suit, is a flashy guide at home in the old, sordid turf in this show written by himself and tensely directed by David Mamet. Indeed, Jay, in his colorful evocativeness, sometimes seems a character invented by Mamet.

Jay wants to prove to us that the arts he celebrates are not only still alive but flourishing.

But he is not just a fascinating historian – he’s also a master magician. He uses audience members for tricks ranging from simple card stunts to vanishing credit cards (which he later returns).

We get the full display of his talents: With his back to a chess board, Jay fills it in with a single knight’s moves – while singing blues songs, reciting a poem and giving cube roots to a number picked at random from the audience.

Jay extracts genuine wonder and juicy joy from the seemingly phony and the aridly cheesy.